Why is "Copy Data Path" path different from the tooltip's path?
Copy Data Path

From 
https://www.blender.org/api/blender_python_api_2_77_release/bpy.types.bpy_struct.html?highlight=id_data#bpy.types.bpy_struct.id_data


  Note that when keying data paths which contain nested properties this must be done from the ID subclass, in this case the Armature rather than the bone.


Or in the case you pointed out from the scene rather than the strip.

To explain using the console, I have a vid seq called blackfoot, it tells me its id_data is the scene. (The bit you mentioned as "left out")

&gt;&gt;&gt; C.scene.sequence_editor.sequences_all['blackfoot'].id_data
bpy.data.scenes['Scene']


Ok now look at frame_start property

&gt;&gt;&gt; C.scene.sequence_editor.sequences_all['blackfoot'].frame_start
1

&gt;&gt;&gt; C.scene.sequence_editor.sequences_all['blackfoot'].path_resolve('frame_start')
1

&gt;&gt;&gt; C.scene.sequence_editor.sequences_all['blackfoot'].path_from_id('frame_start')
'sequence_editor.sequences_all["blackfoot"].frame_start'


The last one looks familiar, it's what you get when you copy data_path, ie the path from the ID data.

Using 

context = bpy.context
scene = context.scene
sequences = scene.sequence_editor.sequences_all


is just IMO good coding practice making the code much more readable 

sequences['blackfoot'].frame_start = 1


than 

bpy.data.scenes['Scene'].sequence_editor.sequences_all['blackfoot'].frame_start = 1


NB. I also use context = bpy.context in test files, to make pasting them into operator or panel code later simple as context is passed by def to just about all methods.